Solve the Boundary-Value Problem, If Possible $$y ^ { tt } + 5 y ^ { t } - 24 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$$

question 113

Multiple Choice

Solve the boundary-value problem, if possible.
$$y ^ { tt } + 5 y ^ { t } - 24 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$$

• A) \(y ( x ) = \left( e ^ { 6 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• B) \(y ( x ) = \left( e ^ { 8 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { x } - e ^ { - 8 x } \right)\)
• C) \(y ( x ) = \left( e ^ { 3 } - e ^ { - 16 } \right) \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• D) \(y ( x ) = \left( e ^ { 3 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• E) No solution

---

Definitions:

Initial Investment

The amount of money used to start a project, purchase assets, or establish a business foundation.

Simple Rate Of Return

A method of calculating the return on an investment without taking into account compound interest or the passage of time.

Cash Operating Costs

Direct expenses incurred during regular operations, such as manufacturing costs, labor, and raw materials, excluding non-cash costs like depreciation.

Automating

involves the use of systems and technology to perform tasks with minimal human intervention.